The grids in general comprise two sets of plates disposed in two orthogonal directions and lap-jointed together to define elementary cells which the fuel rods and the tie-rods pass through. The plates are furthermore connected, at their periphery, to a belt having the same form as the plates. To ensure cohesion of the grids, these component parts are connected together at their intersections. This operation is often carried out at the present time by manual brazing, i.e., by a long and tedious operation, which moreover does not guarantee fully satisfactory reproductibility, even if a relative holding jig is used, such as the one described in U.S. Pat. No. 4,111,348, for constructing grids whose plates are cut out so as to form springs bearing on the fuel rods, or in French Pat. No. 2,364,729.